Attitude estimation from Kalman filter using sensor fusion via data from a gyroscope and accelerometer, providing angular velocity and a reference direction (direction of gravity), respectively. In the third of my three-part series, we first go over a MATLAB example of estimating position and velocity from noisy position data (altitude from sonar). We compare the estimated velocity with that from a finite-difference estimate and find the Kalman filter's is much smoother.

Finally, we discuss the problem of estimating attitude, and formulating the system model. We find that 3-2-1 Euler angles (yaw, pitch, and roll) are not a good state variable x as their evolution equation is not linear in x. However, quaternions q (i.e., Euler parameters ß) are a good attitude representation because their kinematic dynamical equation is linear. A gyroscope provides the angular velocity, ω, as measured in the body-fixed frame for a vehicle, spacecraft, or aircraft. Combining ω with a reference direction g that provides roll and pitch, we demonstrate the use of sensor fusion (from a gyroscope and accelerometer, respectively).

For both examples, construct a system model via the state transition matrix A, the state-to-measurement matrix H, and estimate the process noise and measurement noise matrices, Q and R.

💻 Get the MATLAB Code https://tinyurl.com/kalmanfilterforbe...

This special lecture series takes us into dynamic attitude estimation, using time-varying gyroscope data, as opposed to the previously covered static attitude estimation, which uses simultaneous measurements of known external objects.

Attitude Determination And Control System (ADCS)

► Next: Moment of Inertia Matrix & Principal Axis Frame | MATLAB Example Calculation
   • Moment of Inertia Matrix & Principal ...  

► Previous, Kalman Filter for Beginners, Part 2 - Estimation and Prediction Process & MATLAB Example
   • Kalman Filter for Beginners, Part 2  ...  

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► Prof. Shane Ross 🌠 aerospace engineering professor, Virginia Tech
Background: Caltech PhD | worked at NASA/JPL & Boeing
Research website for ‪@ProfessorRoss‬
http://shaneross.com

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► Space Vehicle Dynamics course videos (playlist)
https://is.gd/SpaceVehicleDynamics

► Lecture notes for Kalman Filter series (PDF)
https://tinyurl.com/kalmanfilterforbe...

► MATLAB Code
https://tinyurl.com/kalmanfilterforbe...

► Reference
Kalman Filter for Beginners: with MATLAB Examples
by Phil Kim (Author), Lynn Huh (Translator), 2010
https://www.amazon.com/dp/1463648359

► Inertial Measurement Unit Used (IMU Sensor)
WIT Motion, Gyroscope + Accelerometer + Magnetometer
https://www.wit-motion.com/gyroscope-...

► Chapters
0:00 Estimating Velocity From Position using Kalman Filter
5:08 Comparison with Finite Differences Approximation for Velocity
9:00 Dynamic Attitude Determination
9:53 WIT Motion Sensor
12:16 Integrating Gyroscope Angular Velocities from Sensor, MATLAB
18:00 Kalman Filter using Yaw, Pitch, Roll Euler Angles
20:30 Kalman Filter using Quaternions (Euler Parameters)
26:16 MATLAB Demo Using Quaternions
30:00 Data Fusion - Accelerometer with Gyroscope
39:01 Sensor Data Fusion Recap

► Courses & Playlists by Dr. Ross

📚Space Vehicle Dynamics
https://is.gd/SpaceVehicleDynamics

📚3-Body Problem Orbital Dynamics Course
https://is.gd/3BodyProblem

📚Space Manifolds
https://is.gd/SpaceManifolds

📚Lagrangian and 3D Rigid Body Dynamics
https://is.gd/AnalyticalDynamics

📚Nonlinear Dynamics and Chaos
https://is.gd/NonlinearDynamics

📚Hamiltonian Dynamics
https://is.gd/AdvancedDynamics

📚Center Manifolds, Normal Forms, and Bifurcations
https://is.gd/CenterManifolds

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